Thursday, October 7, 2010

Logic: Chinese Paradox

In China, we find Daoists, Logicians and Chan/Zen Buddhists showing the skeptical side of logic and human thought that we have already seen in India (Jainism & Buddhism) and Greece (Heraclitus, Pyrrho and Sextus Empiricus).


The Dao De Jing (formerly the Tao Te Ching) is the book by the fist Daoist patriarch Lao Zi (600 BCE) according to tradition. This book and the book of the second Daoist Patriarch Zhuang Zi (370-300 BCE) have many excellent examples of paradox and contradiction. We will consider some of these before the paradoxes of the Chinese logicians Hui Shih and Kung-Sun Lung.

Chapter 11 of the Dao is one of my favorites. It tells us that a wheel is only useful because of the hole in the center. The same is true of a jar made of clay, and the space in a room as well as the doors and windows. We naturally think of things as positives, as beings, but non-being, the holes and emptiness, goes hand in hand with the being. These things (as well as everything else, the text suggests) are and are not in very specific ways. The wheel is both solid and empty at the same time, but not in all of its parts equally. Positive and negative, being and non-being, work together to make things what they are.

If positivism tries for black and white judgments, all yes or all no, and skepticism tries for relative judgments, some yes and some no, this teaching on the wheel and the jar tells us that the solid objects that surround us, the things about which we are most certain, are somewhat and are not somewhat!

There is a Buddhist koan that says at first we see a thing as a thing, then after practice and contemplation we see the thing as a non-thing (a concept, or illusion), and then after further practice and contemplation we again see the thing as a thing (but also, in this third stage, as also a non-thing, our conception). Hegel, whose logic we will learn later, sees this same three-fold process in every stage of individual thought and history of philosophy. At first, if asked, the wheel is a thing, not a nothing or non-thing. Then, we see the hole when it is pointed out to us. Finally, we can see that the solidity and the emptiness of the wheel are both necessary and essential to the wheel being what it is together.

In the Zhuang Zi there are many excellent passages that back up this two-sided view. There are many parts of the text that are almost identical to fragments of Heraclitus. Both Zhuang Zi and Heraclitus say that things can be good to some and bad to others at the same time, dependent on the perspective of the viewer. Heraclitus says that salt water is poisonous for us to drink, but not for the fish who require it to live and breathe. Heraclitus also says that pigs like to bathe in filth. Zhuang Zi asks us which animal knows what tastes good if each eats something different? He says that birds like to sleep in trees, but humans certainly do not. Both thinkers say that humans are ugly to non-humans. Zhuang Zi says that the beautiful women of legend frightened minnows, deer and birds. Clearly, human beauty is of no matter to animals who find us frightening and ugly.

One passage I love asks if words say something or nothing and compares them to the peeps of baby birds. It goes on to say that a sage has a this and a that, but a sage’s this also has a that, and a sage’s that also has a this. Speaking of the Confucians and the Moists (two competing schools of Chinese thought at the time the text is being written) it says that what one calls right the other calls wrong, but we should right their wrongs and wrong their rights. Notice how similar this is to chapter 11 of the Dao. It suggests that a sage would see the wrong to a right and the right to a wrong, would see how something said is both meaningful and meaningless.

Another passage asks if the one who wins an argument is necessarily right, or if there must be one who is right and one who is wrong (remember the Nyaya form of debate and Gotama and Aristotle teaching tactics of debate).

Another passage which is important for the logicians to follow says that among the 10,000 things (the number signifies all, like “a billion” today) there are none that are not big, small, right, wrong, useful and useless. If we consider relativity, any particular thing must be bigger that some other thing and smaller than some other thing. If right and wrong, useful and useless are similarly relative, then the sage should see the back and forth, the some and some not to each of these in considering each individual thing.


Hui Shih (380-305 BCE) is very similar to the Greek thinker Zeno. Both consider paradoxes of relativity in size, motion and other basic properties of things. When he says that heaven or the sky is as low as the earth, he is pointing out that the two meet in the middle, and so low and high are in a particular place equally low and high. When he says one goes to the state of Yueh today and arrives there yesterday, this is a famous puzzle that is quite like the wisdom tales we read in the beginning of the semester: if one crosses the border of Yueh at the stroke of midnight, then one was in Yueh and not in Yueh both today and yesterday, so one could say that one was going there today and arrived yesterday.

The paradox that is most impressive is the Lesser and Greater Similarity and Difference which many have said is similar to observations made in fractal geometry and chaos theory. He says that a great similarity is different from a small similarity, the lesser similarity and difference, but at the same time all things are similar to one another and different from one another, the greater similarity and difference. Consider a bowl with two apples and two oranges. An apple is quite similar to an orange in many ways but it is also different in many ways (the lesser). Anyone can tell that two apples are more alike than an apple and an orange, just as two oranges are more alike than an orange and an apple (this is the lesser similarity and difference). However, on the other hand, it is also true that any two apples are alike and yet different as any two oranges are alike and yet different (this is the greater similarity and difference). Notice that this means the first apple is similar and different to the second apple as well as to an orange. Viewed in a black or white way, the apples are the same and the apple and orange are different, but it is also true to say that the apples are different and the apple and orange are similar.

Kung-sun Lung (325-250 BCE) gives us the famous A White Horse Is Not A Horse argument. Many say that this argument is faulty, but if we follow the thinking of the Daoists and Hui Shih we can see what Kung-Sun is trying to say. He does not mean that a white horse is not in any way a horse, but that in one particular way “a white horse” is not the same thing as “a horse”. He argues that if one brings us a yellow horse, it would not fit the description “a white horse” but it would do fine for the description “a horse”. The two are thus different sets and are not identical though one set is a subset of the other. This means that “a white horse” is and is not “a horse” (in one way “is” and in another way “is not”), and so he can truly say that “a white horse is not a horse”.

Consider that your finger is you but also is not you. If we use “is” in terms of strict identity (like Clark Kent is Superman) then your finger is not you because you are much more than a finger. However, if we use “is” to mean a part incorporated within a thing (like a tree is green) then your finger is oneself because it is part of you. Bill Clinton famously tried explaining this with his “that depends what your definition of ‘is’ is”. Being an individual human, you are and are not humanity. In fact, you are only one human out of quadrillions so far, so you are very much NOT humanity, but what are you more than a human, thus of humanity?


Hui-Neng (683-713 CE) became one of the central patriarchs of the Chan (Zen in Japanese) Buddhist tradition by outdoing his fellow student in a poetry competition to see who had the superior understanding and would succeed the master. The student who everyone expected to be the next master wrote:

The body is the tree of enlightenment, The mind is like a clear mirror-stand.
Polish it diligently time and again, Not letting it gather dust.

Hui-Neng was illiterate as well as a southerner who was considered different and inferior by the other students. After having a boy read the first submitted verse to him, he composed his reply:

Enlightenment originally has no tree, And a clear mirror is not a stand.
Originally there is not a single thing, Where can dust gather?

The master called Hui-Neng and said that this verse showed the superior understanding. Consider the similarity of this exchange to chapter 11 of the Dao and the Zhuang Zi.

Joshu (780 CE) is my favorite Chan/Zen thinker. Many of his short quotes became focal koans for study by students of Zen. I will read passages in class.

(69, 77, 79, 177, 182, 222, 232, 291, 352, 370, 431, 470)